1. The best thing (that/which) I've learned this year was something about myself.

(Which one was missing in the parentheses, that or which? Are both expressions can be used?)

2. The best thing I've learned this year is the Korean language.

( I've leanred the Korean language this year. I know Korean. This is the best thing. { I explained #2 like this. Is it correct? I want to know about the meaning of 'the present perfect' in Sentence 2.}

1. "that" is better, but frankly I'd leave it out entirely!

2. Yes, this is correct.

The present perfect has the helping verbs "have" or "has" and indicates that the action (in this case, "learned") started in the past and continues into the present.
http://www.englishpage.com/verbpage/presentperfect.html

1. In the sentence, either "that" or "which" can be used, depending on the context and the intended meaning.

- If you want to imply that there are multiple things you have learned and you are specifying which one, you would use "that." For example, "The best thing that I've learned this year was something about myself."
- If you want to emphasize the unique quality or significance of the thing you have learned, you would use "which" with a comma before it. For example, "The best thing I've learned this year was something about myself, which has completely changed my perspective."

2. Your explanation for #2 is correct. In sentence #2, the present perfect tense "I've learned" indicates an action that started in the past (learning Korean) and continues to the present (knowing Korean). It implies that you have completed the action of learning Korean and now possess the knowledge of the language. So, in this context, the "present perfect" implies the completion of the action with a connection to the present.